I've been looking for R packages that allow one to fit a logistic mixed model with an AR-1 correlation structure. I've found that it seems easy to do a logistic mixed model or to fit a linear mixed model with such a structure, but not both. Am I wrong in this, and if I'm not; what would an alternative be?
The following simulates and fits a model where the linear predictor in the logistic regression follows a zero-mean AR(1) process, see the glmmTMB package vignette for more details.
> library(glmmTMB) > set.seed(1) > n <- 1000 > size <- 10 > eta <- arima.sim(list(ar=.8),n) > y <- rbinom(n, prob=plogis(eta), size=size) > group <- factor(rep(1,n)) > time <- factor(1:n) > fit <- glmmTMB(cbind(y,size-y) ~ -1 + ar1(time + 0|group), family=binomial) > summary(fit) Family: binomial ( logit ) Formula: cbind(y, size - y) ~ -1 + ar1(time + 0 | group) AIC BIC logLik deviance df.resid 4329.5 4339.3 -2162.8 4325.5 998 Random effects: Conditional model: Groups Name Variance Std.Dev. Corr group time1 2.528 1.59 0.77 (ar1) Number of obs: 1000, groups: group, 1